Intelligent Application of Frozen Food Process Production in the Digital Era

The use of modern freezing technology, in the shortest possible time, the temperature of the food will be lowered to its freezing point below the expected freezing temperature, so that it contains all or most of the water, with the internal heat of the food dispersed to form ice crystals, in order to reduce the life activities and biochemical reactions necessary for the liquid water, inhibit microbial activities, and highly slow down the biochemical changes in food, so as to ensure that the food in the process of cold storage stability. The stability of food in the process of refrigeration is ensured.

Food quick-freezing is the center of the food temperature is quickly frozen to -1 ℃ ~ -5 ℃, through the maximum ice crystal generation belt time required for no more than 30 minutes. Fresh fish and meat with high water content of food, when the product temperature reaches -1 ℃, the water in the food began to freeze, the temperature dropped to -5 ℃, the water contained in 80% of the freeze, then, the whole food roughly become frozen state. Therefore, the temperature limit between -1℃ and -5℃ is called the maximum ice crystal generation zone.

The distance from the surface of the food to the center point divided by the quotient of the time required to reduce the center product temperature from -1°C to -5°C, generally expressed in cm/h.

The freezing point of food is related to the freezing point of the solution contained in the food, and the freezing point of a liquid is the temperature at which the liquid phase is in equilibrium with the solid phase. The vapor pressure of a solution is lower than that of a pure solvent (water), so the freezing point of a solution is lower than that of a pure solvent, and the freezing point of a food is lower than that of pure water. The composition of various foodstuffs varies, so their freezing points are different, and most natural foodstuffs have a freezing point of 0℃ ~ -2.6℃. Freezing point temperature at 0 ℃ water, collard greens; -0.5 ℃ cauliflower, beans; -1.5 ℃ carrots, fish; -2 ℃ of the potato; -2.5 ℃ of the veal, mutton; -3.5 ℃ of garlic, bananas, coconut; -7°C of pecans; -8.5°C of peanuts.

The main effects of freezing on food quality are: 1)

Changes in food volume, liquid food and milk when frozen, the volume will expand.

Freezing can cause various changes within the cells of microorganisms in food, where free water forms ice crystals, which have a mechanical damaging effect on microbial cells. Temperatures below -18°C prevent the growth of almost all microorganisms. Accelerating the freezing speed when ice crystals are formed below the freezing point reduces the effect of ice crystals on food quality. Food before freezing due to the role of various enzymes to produce chemical reactions and cause changes, such as enzyme action in vegetables to cause flavor, color, vitamins and other changes. Quick-freezing can blunt the enzyme activity to a large extent, reducing the impact of enzymes on food.

A fuzzy set is defined as follows:

Let U be a set (either discrete or continuous), denoted by {μ}$$\left\{ \mu \right\}$$, U is called the thesis domain, and μ denotes the elements of the thesis domain [31]. The fuzzy set A in the argument domain U is denoted by the affiliation function μ_A, i.e.: 2μA:U→[0,1]$${\mu_A}:U \to [0,1]$$

A fuzzy set A in the domain U can be represented by an element μ and its affiliation function: 3F={u,μA(u)|u∈U}$$F = \{ u,{\mu_A}(u)|u \in U\}$$

The following types of affiliation functions are commonly used: 1)

Gaussian

This is the most commonly used fuzzy distribution [32]. It is described by two parameters and can be generally expressed as: 4μx=exp[−(x−a)2/σ2](σ>0)$${\mu_x} = \exp \left[ { - {{(x - a)}^2}/{\sigma^2}} \right](\sigma > 0)$$

1)

Fuzzy logic

Fuzzy logic is developed on the basis of two-valued logic and three-valued logic. For a proposition, it is either “true” or “false”, and one of the two must be true, which is two-valued logic.

A fuzzy subset R of Eq. is known as the fuzzy relation from U to V, also known as the binary fuzzy relation.

It can be characterized by the following affiliation function 8μR:U×V→[0,1]$${\mu_R}:U \times V \to [0,1]$$

(2)

Representation of fuzzy relationships a)

Fuzzy set representation

Fuzzy relations are also fuzzy sets, so fuzzy relations can be represented by the fuzzy set representation in equation (9). 9R=∑μR(u,v)(u,v)(u,v)∈U×V$$R = \sum {\frac{{{\mu_R}(u,v)}}{{(u,v)}}} \quad (u,v) \in U \times V$$

If the [INDEX] operator in the formula represents “take a small one min” and v represents “take a big one max” operation, this synthesis relationship is the maximum-minimum synthesis, synthesis relationship R = P · Q. 5)

Fuzzy reasoning

According to the fuzzy set theory and fuzzy logic theory, establishing fuzzy statement and reasoning about it is an important content of designing fuzzy control system, according to the given grammatical rules to form a statement containing fuzzy concepts is called fuzzy statement, which is the carrier of fuzzy rules.

The main work of the structural design of the fuzzy PID controller is to determine the input module and output module of the fuzzy controller.

When designing the input module, the number of input variables of the fuzzy PID controller is usually distinguished by the number of dimensions of the fuzzy PID controller, and the common fuzzy PID controller can be divided into three forms according to the number of dimensions of the fuzzy PID control system. In this paper, the control system uses a two-dimensional fuzzy PID controller.

After determining the structure of the fuzzy PID controller, the two inputs sampled into the controller have to be fuzzified in order to implement the fuzzy algorithm.

Because the fuzzification function has a large impact on the performance of the control system, it should be selected according to the actual situation and repeated trials. After the selection of the fuzzification function B, it is also necessary to determine the definition domain of the fuzzy function of each fuzzy subset of the input quantities, so that the number and range of the fuzzy subsets should be spread throughout the entire input quantities of the theoretical domain, so that there is a corresponding fuzzy function for all inputs most.

The control rules are the core part of the fuzzy PID controller, which consists of three parts: selecting the set of words describing the input and output variables, defining the fuzzy subsets of the fuzzy variables, and establishing the control rules of the fuzzy controller. 1)

Selection of the set of words describing the input and output variables

Because the control rules of the fuzzy PID controller are expressed as a set of fuzzy conditional statements, by adding large, medium, and small to the positive and negative directions and considering the zero state of the variables, there are seven vocabularies, namely:

{negative large, negative medium, negative small, zero, positive small, positive medium, positive large} 11{ NB NM NS ZE PS PM PB}$$\left\{ {\begin{array}{*{20}{c}} {NB}&{ NM}&{ NS}&{ ZE}&{ PS}&{ PM}&{ PB} \end{array}} \right\}$$

Among them:

RMIMOi$$R_{MIMO}^i$$ if (x is A_i and ⋯ and y is B_i) then (z_i is C_i, ⋯, z_q is D_i).

The preconditions of RMIMOi$$R_{MIMO}^i$$ constitute a fuzzy set A_i × ⋯ × B_i on a direct product space X × ⋯ × Y and the conclusion is a merge of q spatial actions which are independent of each other. Thus, rule i can be expressed as the following fuzzy implication relation: 13RiMIMO:(Ai×⋯×Bi)→(Ci+⋯+Di)$${R^i}_{MIMO}:({A_i} \times \cdots \times {B_i}) \to ({C_i} + \cdots + {D_i})$$

Thus the rule R can be expressed as: 14R = {∪i=1nRiMMO} = {∪i=1n[(Ai×⋯×Bi)→(Ci+⋯+Di)]} = {∪i=1n[(Ai×⋯×Bi)→Ci,⋯,(Ai×⋯×Bi)→Di)]} = {RBMSOl,⋯,RBMSOq}$$\begin{array}{rcl} R &=&\left\{ {{{\bigcup\limits_{i =1}^n {{R^i}} }_{MMO}}} \right\} \\ &=&\left\{ {\bigcup\limits_{i =1}^n {\left[ {({A_i} \times \cdots \times {B_i}) \to ({C_i} + \cdots + {D_i})} \right]} } \right\} \\ &=&\left\{ {\bigcup\limits_{i =1}^n {\left[ {({A_i} \times \cdots \times {B_i}) \to {C_i}, \cdots ,({A_i} \times \cdots \times {B_i}) \to {D_i})} \right]} } \right\} \\ &=&\left\{ {RB_{MSO}^l, \cdots ,RB_{MSO}^q} \right\} \\ \end{array}$$

There are usually several types of commonly used clarity calculations: 1)

Maximum affiliation function method

If there is only one peak in the affiliation function of the fuzzy set C′ of the output quantity, then the maximum value of the affiliation function is taken as the clarity value, i.e.: 15μ(C′)(z0)≥μC′(z)z∈Z$${\mu_{({C^\prime })}}({z_0}) \ge {\mu_{{C^\prime }}}(z)\quad z \in Z$$

Where, z₀ denotes the clear value, if the affiliation function of the output quantity has more than one extreme value, then the average of these extreme values is taken as the clear value. 2)

Median method

The so-called median method is to take the median of μ_c(z) as the clear quantity of z, i.e., the median of z₀ = df(z) = μ_c(z), which satisfies ∫0zμ(C)(z)dz=∫bμ(C)(z)dz$$\int_0^z {{\mu_{(C)}}} (z)dz = \mathop \smallint \nolimits^b {\mu_{(C)}}(z)dz$$, that is to say, with z as the demarcation, the μ_c(z) on both sides of the demarcation line is equal to both sides of the area enclosed by the horizontal axis.

Because this method is similar to the calculation of the center of gravity of an object in physics, it is also called the center of gravity method. For the case where the domain of the argument is discrete, we can treat it similarly, and the same is true: 17z0=∑i=1nziμC(zi)∑i=1nμC(zi)$${z_0} = \frac{{\sum\limits_{i = 1}^n {{z_i}} {\mu_C}({z_i})}}{{\sum\limits_{i = 1}^n {{\mu_C}} ({z_i})}}$$

The coding of parameters contains three parts: coding of the affiliation function, coding of the control rules, and coding of the scaling and quantization factors. 1)

Coding of affiliation function

The affiliation function used in the fuzzy controller designed in this paper is that the Z-type affiliation function is used at the head, the S-type affiliation function is used at the tail, and the triangle affiliation function is used in the middle. Since three vertices determine the shape of a triangle, the optimization objective in this paper is the horizontal coordinates of the vertices.

The complexity of the fitness function affects the complexity of the whole algorithm, and its selection directly affects the convergence speed of the algorithm and determines whether the optimal solution can be found, which can also be called the evaluation function [34]. Evaluation of the lyophilizer shelf temperature control system is mainly measured by the accuracy and stability and rapidity. Therefore, the fitness function is designed as shown in Eq. (18) and Eq. (19): 18J=∫0∞(w1|e(t)|+w2u2(t))dt+w3tu$$J = \int_0^\infty {({w_1}|e(t)| + {w_2}{u^2}(t)){d_t}} + {w_3}{t_u}$$ 19f=1/(J+e−10)$$f = 1/(J + {e^{ - 10}})$$

Eq:

t_u - the rise time of the system;

e(t) - the value of the deviation of the system, e(t) = rin(t) − yout(t);

u(t) - the output of the controller of the system;

w_i - the weights of the items, i = 1, 2, 3.

After the determination of the fitness function is completed, the fitness of all individuals within the population can be obtained, and then according to the roulette wheel selection method can be calculated that the individual is selected to the probability of p=fi/∑fi$$p = {f_i}/\sum {{f_i}}$$. At the same time, in order to avoid the loss of high-quality individuals, the high-quality individual preservation strategy will be adopted, which is to allow the individual with the largest fitness value to be directly preserved in a specific variable without crossover mutation. Since the populations need different probabilities for crossover and mutation during evolution, the strategy of automatically adjusting the probability of crossover mutation with the number of evolutionary generations is adopted to avoid the algorithm from converging too slowly or falling into the local optimal solution too early. The decreasing algorithm is used for crossover that way, and the increasing algorithm is used for mutation probability. When cross-mutating the control rules, the resulting decimals need to be subjected to rounding and range limiting operations.

The corresponding closed-loop negative feedback control process under the action of the PID controller is shown in Fig. 2. It can be seen that the reflection curve after 1500 seconds in the stabilization, taking too long.

Figure 2.

Curves of fractional PID controller with the input of step signal

The control indicators are shown in Table 1. The overshoot is as high as 9% and the regulation time is above 900 seconds. The maximum deviation also reaches 0.65°C.

Because of the complexity of building the fuzzy genetic PID controller directly with the module, this paper uses the form of S-function to construct the module, the number of state variables is 1, and the number of outputs is chosen to be 5, taking into account the displayed changes in the variables Kp, Ki, Kd coefficients.

The corresponding closed-loop negative feedback control process under the action of fuzzy genetic PID controller is shown in Fig. 3.

Figure 3.

Simulink of fuzzy fractional PID controller with the input of step signal

Table 2 shows each control index of the fuzzy genetic PID controller.

Comparison of Table 1 and Table 2 can be found that the fuzzy genetic PID controller has the best control effect, the regulation time, overshooting, maximum deviation value and other indicators of excellent performance, and its room temperature change curve is smoother, the control effect is more ideal.

Fig. 4 and Fig. 5 are the change curves of five parameters Kp, Ki, Kd,λ,μ of the fuzzy genetic PID controller in the process of cooling water temperature difference control, observing the curve diagram, we can easily find that these parameters are constantly changing before the cooling water temperature difference reaches the set value, and basically remain unchanged after the temperature difference reaches the set value.

Figure 4.

Curves of fuzzy fractional PID controller’s parameters Kp and Kd

Figure 5.

Curves of fuzzy fractional PID controller’s parameters Ki and λ,μ

Fig. 6 and Fig. 7 show the step response curves when the temperature difference set value is 4°C and 3°C respectively. Observing the curves in the figures, it can be seen that the fuzzy genetic PID controller still has good control quality when the cooling water temperature difference set value is changed.

Figure 6.

Simulink of fuzzy fractional PID controller with the input of step signal

Figure 7.

Simulink of fuzzy fractional PID controller with the input of step signal

In the actual food refrigeration system, the cooling water piping system is dynamically changing, which leads to changes in the cooling water piping characteristic curve, Figure 8 is the transfer function changes (corresponding to the actual cooling water system piping characteristic curve changes) when the step response curve, observe the curve in the figure can be seen, in the system piping characteristics change, the fuzzy genetic PID controller is still a good performance. The parameters of the traditional PID controller remain fixed after the end of the system commissioning stage, which makes the actual cooling water temperature difference control quality decline. From the above comparison results, it can be seen that the fuzzy genetic PID controller with dynamically changing parameters is of high value for the temperature difference control of the actual cooling water system with dynamically changing piping characteristic curves.

Figure 8.

Room temperature response curve